Accurate measurements of fluid viscosities are important in many industries. In the oil and gas industry, for example, it is often necessary to obtain accurate measurements of the viscosity of the liquid hydrocarbons found in a subterranean formation. Hydrocarbon liquids found at some of the shallower depths beneath the surface of the earth can have viscosities ranging up to a million centipoise (mPa.s). Extraction of such viscous oils from the formation usually involves production techniques which rely upon lowering the viscosity of the hydrocarbons. In order to design such production techniques, it is necessary to measure oil viscosity at varying temperatures and pressures which approximate to the range of formation conditions.
Capillary viscometers of the types disclosed in U.S. Pat. No. 3,081,621 issued to N. A. De Bruyne; No. 3,116,630 issued to J. J. Piros; and No. 3,375,704 issued to B. T. Thompson, Jr. et al., may be utilized to measure the viscosity of a fluid. These devices are functional to measure the viscosity of the fluid flowing through the capillary by measuring the pressure drop across the capillary under steady-state flow conditions at a known flow rate.
In a variation of this technique, viscosity may be determined by maintaining a constant pressure drop across the capillary and measuring the time required for a predetermined volume of fluid to flow therethrough. Exemplary of such devices are those shown in U.S. Pat. No. 4,302,965 issued to T. W. Johnson et. al.; No. 3,699,804 issued to H. U. Gassmann et. al. and No. 3,353,403 issued to F. H. Deily et. al.
Alternative arrangements involve the use of two or more capillaries in series or parallel. Such viscometers are described, for example, in U.S. Pat. No. 3,808,877 issued to D. E. Blair; No. 3,798,960 issued to J. R. Glass; No. 4,578,990 issued to S. D. Abbott et. al. and No. 2,934,944 issued to D. Eolkin.
All of the viscometers disclosed in the above-mentioned patents rely on the Hagen-Poiseuille law, which states: ##EQU1## where: .mu. is the viscosity of the fluid flowing through the capillary tube;
.DELTA.p is the pressure head; PA1 R is the capillary tube radius; PA1 L is the length of the capillary tube; and PA1 Q is the rate of fluid flow through the capillary tube. PA1 the flow is laminar; PA1 the fluid density is constant (i.e. "incompressible flow"); PA1 the flow rate is constant (i.e. "steady state"); PA1 the fluid behaves as a continuum; PA1 no slip exists at the wall; and PA1 the end effects are negligible. PA1 providing a rapid indicia of viscosity; PA1 being adapted for transient flow conditions, thereby eliminating the requirement for `steady state` conditions and hence for provision of means for generating constant flow rate or means for maintaining a constant differential pressure across the capillary; and PA1 reducing the requirement for large volumes of test fluid. PA1 R is the radius of the capillary tube; PA1 L is the length of the capillary tube; PA1 Pu is the pressure in the upstream vessel; PA1 Pd is the pressure in the downstream vessel; and PA1 .mu. is the viscosity of the fluid filling the capillary tube. PA1 V is the volume of the liquid originally in the upstream vessel; PA1 t is the time; and PA1 Pu is the pressure in the upstream vessel. PA1 .DELTA.P(t=o)=(Pu-Pd) at time zero;
It will be appreciated that the Hagen-Poiseuille law is strictly valid only when the following conditions are satisfied, namely:
In summary, therefore, these prior art methods for measuring viscosity involve varying only a single parameter in the Hagen-Poiseuille equation. From this parameter the viscosity measure is derived. This variable may be either the pressure drop across the capillary, the flow rate, or the time required for a given volume of fluid to pass through the capillary. Such methods thus require provision of a means for generating a predetermined constant flow rate (usually a constant rate pump), or means for maintaining constant differential pressure across the capillary (usually constant fluid head).
Additionally, to ensure the integrity of the equation, it is necessary to achieve steady state flow conditions.
Whilst such methods are well adapted for many fluids, they are not suitable for highly viscous heavy oils and the like. The problems inherent with these methods are associated with difficulties in pumping viscous fluids and in measuring flow rate at high pressures and elevated temperatures. Additionally, the attainment of steady state flow conditions, which may take several hours, is time-consuming. Another disadvantage is that relatively large volumes of test fluids may be required.
Rotational or vibrational viscometers, which may provide an alternative, are expensive and difficult to use at high temperatures and pressures.
There exists therefore the need for a method and apparatus suitable for determining the viscosity of highly viscous fluids at elevated temperature and pressure having the characteristics of:
By `transient` flow conditions is meant that as a pressure differential between two points progressively decreases, or decays, there is a concomitantly diminshing flow rate associated therewith. Stated otherwise, there is more than one parameter, used in the Hagen-Poiseuille equation, which is varying.